The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation

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3answers
503 views

Why is $ \vec{S}^{(A)} \otimes \vec{S}^{(B)} = \frac{\hbar^2}{4}(\sigma_x \otimes \sigma_x + \sigma_y \otimes\sigma_y + \sigma_z \otimes \sigma_z)$?

I haven't been taught tensor product in class but they have taught us addition of spin. I looked up online in this link->http://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_7.pdf (pg ...
4
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1answer
97 views

Clebsch-Gordan Coefficients for two spin-1 particles - Why is there a ∣0⟩∣0⟩ ket?

I have used the rules for addition of angular momenta to work out the Clebsch-Gordan coefficients, which all seem right except for state $\lvert0,0\rangle$: For n = 1 \begin{align} \lvert1,1\rangle ...
4
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2answers
198 views

Ten-ping bowling: Can a ping pong ball knock over a bowling pin?

In this video we see a rather unorthodox bowling technique on display. The gentleman appears to knock over all of the pins using only a ping pong ball. It's a fake, of course: you could never knock ...
2
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1answer
163 views

Why the orbital angular momentum equal zero for electron in s state? does it mean that the electron doesn't orbiting in s [duplicate]

Why is the orbital angular momentum $l$ equal to zero for electrons in the $s$ state? Does it mean that the electrons aren't actually orbiting?
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1answer
96 views

Conservation of total angular momentum in $\Phi$-meson decay

I am looking into the decay of a $\Phi$-meson decaying into $K^+$, $K^-$. My problem is, the $\Phi$-meson has a total angular momentum of 1 and the two Kaons have a total angular momentum of 0. On the ...
2
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2answers
104 views

Intuition Behind Conservation of Angular Momentum

I'm having a fairly hard time understanding the intuition behind Noether's derivation of the conservation of angular momentum from the rotational invariance of the Lagrangian, though I do understand ...
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1answer
46 views

Orbital angular momentum and multielectron atoms energies

Explain why states with different orbital angular momentum quantum number have different energies for multielectron atoms but are degenerate in energy for hydrogen Can anyone explain?
2
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5answers
624 views

How does a spinning electron produce a magnetic field?

I learned in my undergraduate physics class that atoms have magnetic fields produced by the orbit of electrons and the spin of electrons. I understand how an orbit can induce a magnetic field because ...
0
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1answer
80 views

What is the inertia caused by angular momentum when twisted on it's rotating axis?

I would like to provide a more thorough answer to this question here http://aviation.stackexchange.com/q/3709 but I realized I don't know enough about angular momentum. If an airplane wheel is ...
7
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2answers
407 views

Quantization of a particle on a spherical surface

Suppose we have a particle of mass $m$ confined to the surface of a sphere of radius $R$. The classical Lagrangian of the system is $$L = \frac{1}{2}mR^2 \dot{\theta}^2 + \frac{1}{2}m R^2 \sin^2 ...
3
votes
3answers
118 views

How is angular momentum conserved if a bullet hits a wheel?

Suppose my system involves: 1) A mounted wheel with some outward flap 2) A bullet already in motion Initially the net angular momentum is 0 and the net kinetic energy is just that of the speeding ...
0
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1answer
76 views

Angular Momentum in Quantum mechanics

In Gasiorowicz's Quantum Physics, we determined the relation: $$L_z | l,m\rangle= \hbar m | l,m \rangle$$ I would like to determine: $\langle l,m_1 | L_x | l,m_2 \rangle $ I thought about expressing ...
2
votes
1answer
39 views

Angular momentum of a black hole

I recently read this Phys.SE post and, since I didn't know that black holes had a spin, a question came to my mind: how can I calculate the spin velocity of a black hole? Does mass or radius affects ...
3
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3answers
215 views

Can a wave possess spin?

Since a matter wave is associated with a particle in quantum mechanics, does the wave spins? I mean, can we visualize the spinning of wave or is it possible that the wave spins?
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2answers
108 views

An electron in $s$ state

If an electron is in $s$ state, for example in 1s state for Hydrogen or 5s state for Silver atom, $\ell=0$. So,its total angular momentum $L$ is also equal to 0. So, what is electron actually doing in ...
3
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1answer
258 views

Angular momentum depends on origin?

The angular momentum of a particle rotating about a point is given by $\vec{L} = \vec{r} \times \vec{p}$. Imagine a particle tracing a circular path on a flat table. If I put the origin of my ...
3
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1answer
88 views

Photon Angular Momentum

Essentially I am wanting to evaluate $$\langle j\, m \mid a^\dagger(\mathbf{k}, \lambda) \mid 0 \rangle \,,$$ where $\lambda$ indicates the circular polarization (about $\mathbf{k}$). We have that ...
2
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1answer
47 views

Does the unit of Inertia include radians? [duplicate]

The unit for angular acceleration $\alpha$ is: $$\mathrm{rad/s^2}$$ The unit for torque is $\mathrm{Nm}$: $$\mathrm{kg\ m^2/s^2}$$ And their relationship with Inertia is: $$I = \tau/\alpha$$ So ...
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0answers
25 views

Lateral forces on earths surface

If a giant stone sphere was sitting on the earths surface, would it experience a later force due to the earths rotation? For example my intuition tells me that if there was a sphere a mile high ...
15
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3answers
1k views

Wouldn't angular momentum of a binary star system decrease?

Consider a binary star system, as these stars go around one another they would emit gravitational waves. Since, the graviton is a spin 2 particle. Wouldn't the angular momentum of the stars decrease? ...
0
votes
1answer
49 views

Coordinate System vs. Angular Properties vs. Centroid

Please help me check my understanding related to the rotational motion of a 3D rigid body after reading some Physics textbooks and googling for some more materials (e.g., Wikipedia's Torque, ...
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1answer
75 views

Confusion about units of angular momentum

According to multiple sources the SI units for angular momentum are kg * m$^2$ / sec I am confused about the derivation for this. Here is what I have done: $$L = I \cdot \omega \\ = m \cdot r^2 ...
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0answers
99 views

Collision of Discs and Snooker Kicks

I woke up this morning thinking about spinning discs. Could someone verify whether my reasoning below is correct? Problem 1 Suppose have two identical uniform discs constrained to move in a plane. ...
0
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1answer
101 views

How to derive the commutation relationship between $\hat{L}^2$ and $\hat{\textbf{p}}$ [closed]

How to prove that $$[\hat{L}^2,\hat{\textbf{p}}] = i\hbar(\hat{\textbf{p}}\times\hat{\textbf{L}} - \hat{\textbf{L}} \times \hat{\textbf{p}})$$ I tried to expand $\hat{L}^2$: ...
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2answers
174 views

Describing a motion of gyroscope with gimbal

Can you tell be how to set the equations to describe the motion of this machine in movie "Contact": https://www.youtube.com/watch?v=TSaO9VGjLXc This is gyroscope with gimbal, am I right?
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1answer
92 views

Angular momentum of two rotating spheres

I am trying to calculate an instantaneous merger of two rotating spheres into one. Two spheres each rotating around their own axis of rotation (which are generally not aligned) and moving relative to ...
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0answers
60 views

Where do $L_+$ and $L_-$ live, if not in $\mathfrak{so(3)}$?

This question is continuation to the previous post. The lie algebra of $ \mathfrak{so(3)} $ is real Lie-algebra and hence, $ L_{\pm} = L_1 \pm i L_2 $ don't belong to $ \mathfrak{so(3)} $. However, ...
2
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3answers
95 views

Instantaneous angular momentum of a disc

Suppose we have a disk of radius $r$ and mass $m$ travelling at velocity $v$. I want to calculate the instantaneous angular momentum with axis through the edge of the disc (on the circumference). ...
0
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0answers
38 views

Calculating the $J$ value for atomic terms, having a lot of trouble with this. Already attempted

I am trying to understand this, and want to be very very clear. This is a homework question but I already attempted to answer it, so please don't put this question on hold. The question What ...
7
votes
4answers
383 views

What's is the origin of Orbital Angular Momentum of electrons in atoms?

Consider the Hydrogen 1s electron. We know that, in the quantum picture, the electron isn't orbiting or rotating at all, rather we simply state that the electron is spread over the entire space with ...
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0answers
40 views

Angular Momentum Expectation in Magnetic Field

I am trying to find the time dependent expectation value for J ($\langle J(t) \rangle$) for a spin 3/2 particle in a uniform magnetic field (in the z direction). My method is as follows: ...
1
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1answer
59 views

Eigenstates of coupled Angular Momentum

SO I have a hamiltonian: $$H=\alpha J_1\cdot J_2$$ And I am asked to find the eigenstates and eigenvalues of this Hamiltonian in terms of products of the eigenstates of the z components of the ...
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0answers
55 views

Angular momentums addition in QM

We know that the spatial inversion parity for eigenfunctions of $\hat {L}_{z}$ operator (spherical functions) is $(-1)^{l}$, where $l$ refers to angular momentum. So for product of two eigenfunctions ...
3
votes
1answer
182 views

Diagonal Hamiltonian of 3 Spin 1/2 Particles

I have three Spin 1/2 Particles and a Hamiltonian given by $$H=A(S_1\cdot S_2)+B(S_2\cdot S_3+S_1\cdot S_3)$$ In order to find the energy spectrum, I want to diagonalize H in terms of ...
2
votes
2answers
228 views

Angular Momentum Operator in Quantum Field Theory

I'm following along with David Tong's QFT course and am trying to derive the result shown in question 6 on his 2nd problem sheet, but am running into problems when applying it to the free real scalar ...
8
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3answers
387 views

Addition of spin angular momentum for massless particles

How do I add the spin angular momentum of massless particles, like photons, where only the transverse polarizations are allowed? If all three polarizations were allowed, this would be an easy ...
3
votes
1answer
231 views

Why have $n$, $\ell$, $m_\ell$, $m_s$ been picked as quantum number symbols $\mathbf{\text{in this order}}$?

I’m learning about electron configurations and don’t quite understand why $n$, $\ell$, $m_\ell$, $m_s$ have been picked as symbols for the quantum numbers. As far as I understand it, the principal ...
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1answer
202 views

Finding angular momentum about the center of mass?

If we have a couple of particles of an equal, unknown mass: $$r_{+} = (c + e^{-Bt} \cos({\theta}))\textbf{x} + (d + e^{-Bt} \sin({\theta}))\textbf{y}$$ $$r_{-} = (c - e^{-Bt} ...
0
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0answers
172 views

Angular momentum of 2d harmonic oscillator

So, I have the problem of determining the spectrum of H and L, in terms of creation and annihilation operators of angular momentum... The problem goes along with what is happening on this page. ...
0
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1answer
75 views

Addition of Angular Momentum

I am tring to find the eigenvectors of a two spin system, with $j_1=3/2$ and $j_2=1/2$. To start, $$m_1 =-3/2,-1/2,1/2,3/2$$ $$m_2=-1/2,1/2$$ For $j_1$, there are 4 possible states, and 2 possible ...
0
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0answers
93 views

Difference between expectation values of $L^2$, $L_z$ and measuring $L^2$, $L_z$

I was given with this hydrogen radial wavefunction $$ R_{21} =\left(\sqrt{\frac{1}{3}}Y^0_1 + \sqrt{\frac{2}{3}}Y^1_1\right) $$ and was asked to find a) What are the expectation values of the ...
0
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0answers
48 views

Spherical Harmonic projection on axis

I am trying to solve for the Spherical harmonics $Y^m_{l=1}$ with a second axis at an angle $\alpha$ with respect to the z axis. Then this can be used to find the probability that a particle with ...
1
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0answers
58 views

How does $\bar{r}\times(\bar{\nabla}\times) - \bar{\nabla}\times(\bar{r}\times)$ relate to the orbital angular momentum operator?

When I attempted to calculate the following by hand $$\bar{r}\times(\bar{\nabla}\times\bar{F}) - \bar{\nabla}\times(\bar{r}\times\bar{F}),$$ I noticed some of the terms I extracted looked similar to ...
0
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1answer
57 views

Construction of Angular Momentum eigenvectors

I have a problem that asks (verbatim) Carryout the construction of the eigenvectors of total angular momentum and its z component for $j_1$=3/2 and $j_2$=1/2 I am not completely sure where to ...
9
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1answer
238 views

What makes a wrist-energized gyroscope rotate faster?

I'm considering a wrist-energized gyroscope, shown below (after my daughter let it fall and it broke open). That one was sold as Roller Ball, but variants are known as Powerball, DynaBee, Dynaball, ...
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1answer
100 views

What is $\langle \sigma_\mu \rangle$ $\langle \sigma_\mu \rangle$ for the Pauli Matrices?

What is \begin{align} \sum_{\mu=0}^{3} \langle \sigma_{\mu} \rangle^2 = ? \end{align} $\sigma_{\mu}$ are the Pauli matrices. The Bra-Ket notation is used in this question: \begin{align} \langle ...
0
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1answer
48 views

Thrust to Weight ratio in Space with an off set CoM

With regards to this thread, Thrust center in space My question is, if the thrust to weight ratio was increased so that it was much higher than the weighted mass of the sphere (ship), would the ...
0
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0answers
65 views

Imagine a 50-mile tower spanning from desert floor to the Karman Line

CORRECTION: The structure weighs 1.568E15 kg.s Does the structure effect the equilibrium of earth's rotation? Would momentum from Earth's rotation apply lateral force to the structure? What else do ...
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2answers
2k views

How can a singularity in a black hole rotate if it's just a point?

I guess nobody really knows the true nature of black holes, however, based on everything I know about black holes, there is a "singularity" at their center, which has finite mass but is infinitely ...
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0answers
75 views

Transforming components of the angular momentum operator

Let me introduce the problem: In a two electron fixed nucleus problem the "body" is the atom, whose electrons are located relative to the nucleus by the coordinates $r_1$ and $r_2$, and the angle ...